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# Licensed under the Apache License, Version 2.0 (the "License");
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import abc
from typing import Any, Callable, Iterable, Tuple, Union
import tensorflow as tf
from ..base import TensorType
from ..experimental.check_shapes import check_shapes
[docs]class GaussianQuadrature:
"""
Abstract class implementing quadrature methods to compute Gaussian Expectations.
Inheriting classes must provide the method _build_X_W to create points and weights
to be used for quadrature.
"""
@abc.abstractmethod
@check_shapes(
"mean: [batch..., D]",
"var: [batch..., D]",
"return[0]: [N_quad_points, batch..., D]",
"return[1]: [N_quad_points, broadcast batch..., 1]",
)
def _build_X_W(self, mean: TensorType, var: TensorType) -> Tuple[tf.Tensor, tf.Tensor]:
raise NotImplementedError
@check_shapes(
"mean: [batch..., D]",
"var: [batch..., D]",
"return: [n_funs..., batch..., broadcast D]",
)
def __call__(
self,
fun: Union[Callable[..., tf.Tensor], Iterable[Callable[..., tf.Tensor]]],
mean: TensorType,
var: TensorType,
*args: Any,
**kwargs: Any,
) -> tf.Tensor:
r"""
Compute the Gaussian Expectation of a function f::
X ~ N(mean, var)
E[f(X)] = ∫f(x, *args, **kwargs)p(x)dx
Using the formula::
E[f(X)] = sum_{i=1}^{N_quad_points} f(x_i) * w_i
where x_i, w_i must be provided by the inheriting class through self._build_X_W.
:param fun: Callable or Iterable of Callables that operates elementwise, with
signature f(X, \*args, \*\*kwargs). Moreover, it must satisfy the shape-mapping::
X shape: [N_quad_points, batch..., d].
f(X) shape: [N_quad_points, batch..., broadcast d].
In most cases, f should only operate over the last dimension of X
:param mean: Array/Tensor representing the mean of a d-Variate Gaussian distribution
:param var: Array/Tensor representing the variance of a d-Variate Gaussian distribution
:param args: Passed to fun
:param kargs: Passed to fun
:return: Gaussian expectation of fun
"""
X, W = self._build_X_W(mean, var)
if isinstance(fun, Iterable):
return [tf.reduce_sum(f(X, *args, **kwargs) * W, axis=0) for f in fun]
return tf.reduce_sum(fun(X, *args, **kwargs) * W, axis=0)
[docs] @check_shapes(
"mean: [batch..., D]",
"var: [batch..., D]",
"return: [batch..., broadcast D]",
)
def logspace(
self,
fun: Union[Callable[..., tf.Tensor], Iterable[Callable[..., tf.Tensor]]],
mean: TensorType,
var: TensorType,
*args: Any,
**kwargs: Any,
) -> tf.Tensor:
r"""
Compute the Gaussian log-Expectation of a the exponential of a function f::
X ~ N(mean, var)
log E[exp[f(X)]] = log ∫exp[f(x, *args, **kwargs)]p(x)dx
Using the formula::
log E[exp[f(X)]] = log sum_{i=1}^{N_quad_points} exp[f(x_i) + log w_i]
where x_i, w_i must be provided by the inheriting class through self._build_X_W.
The computations broadcast along batch-dimensions, represented by [batch...].
:param fun: Callable or Iterable of Callables that operates elementwise, with
signature f(X, \*args, \*\*kwargs). Moreover, it must satisfy the shape-mapping::
X shape: [N_quad_points, batch..., d].
f(X) shape: [N_quad_points, batch..., broadcast d].
In most cases, f should only operate over the last dimension of X
:param mean: Array/Tensor representing the mean of a d-Variate Gaussian distribution
:param var: Array/Tensor representing the variance of a d-Variate Gaussian distribution
:param args: Passed to fun
:param kwargs: Passed to fun
:return: Gaussian log-expectation of the exponential of a function f
"""
X, W = self._build_X_W(mean, var)
logW = tf.math.log(W)
if isinstance(fun, Iterable):
return [tf.reduce_logsumexp(f(X, *args, **kwargs) + logW, axis=0) for f in fun]
return tf.reduce_logsumexp(fun(X, *args, **kwargs) + logW, axis=0)